What makes the Phillips-Perron test different from ADF?

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AcadiFi · Accepted Answer

The Phillips-Perron (PP) test, like ADF, tests for a unit root with null of non-stationarity. The key difference is how each test handles autocorrelation and heteroskedasticity in residuals. ADF adds lagged difference terms (parametric correction); PP uses a non-parametric correction applied directly to the test statistic based on the long-run variance estimated via Newey-West or Bartlett kernels. The PP regression is Δyt = α + βt + γ yt-1 + et without augmentation.

PP is robust to general forms of serial correlation and heteroskedasticity without requiring specification of lag length for augmentation—only bandwidth for variance estimation. In finite samples, PP can have size distortions with negatively autocorrelated residuals, while ADF handles these better. Conversely, PP handles heteroskedasticity more gracefully than ADF.

Both tests share the same asymptotic distribution and MacKinnon critical values. Results usually align but can differ in borderline cases. Many practitioners run ADF, KPSS, and PP together—if all three concur (ADF rejects non-stationarity, PP rejects non-stationarity, KPSS fails to reject stationarity), conclude stationarity confidently. Disagreement signals regime shifts, structural breaks, or fractional integration that standard tests miss. For such cases, consider Zivot-Andrews (structural break) or ADF-GLS (improved power). Software implementations typically report lag selection (ADF), bandwidth (PP), and kernel choice. Default settings often perform well for typical financial data.

What makes the Phillips-Perron test different from ADF?

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